I have to organize a small sports league and I am puzzled on how to create the game plan.
We are 8 persons playing table soccer with 2 vs. 2 matches. The idea is that each person plays once with every other person. So e.g. person 1 will play once with person 2, 3, 4, 5, 6, 7 and 8. So there are 7 matchdays and 2 games on each. If a team wins both players receive a point. At the end of the season a player can have earned a max of 7 points.
E.g. matchday 1: p1&p2; p3&p4; p5&p6; p7&p8 E.g. matchday 2: p1&p3; p2&p4; p5&p7; p6&p8
How can I calculate the teams for each of the seven game days given the conditions above? Since the strongest two teams would play against each other depending on points collected in the earlier games I only need a set of 4 teams for each matchday.
I would be grateful for some smart help on calculating a game plan. I guess I am stuck here:
players = Range[1, 8]; teams = Select[Subsets[players , 2], Length[#] == 2 &];
Thanks a lot Patrick